The Poincare-Birkhoff theorem and some of its application

有關Poincare-Birkhoff定理及其應用

葉宇軒(Yu-Hsieh Yek)

指導教授 ： 陳國璋

國立清華大學/理學院/數學系/碩士(2010年)

https://doi.org/10.6843/NTHU.2010.00085

摘要

In this article we investigate various versions of
the Poincare-Birkhoff theorem
and briefly describe its history.
We present detailed proof for a generalization by J. Frank.
We also study some applications of the Poincare-Birkhoff theorem to differential equations.

關鍵字

Poincare-Birkhoff定理 ； 固定點

並列摘要

無資料

並列關鍵字

Poincare-Birkhoff theorem ； twist map

參考文獻

[1] G.D.Birkho, An extension of Poincare's last geometric theorem, Acta math. 47(1925),297-311

[2] W.Y.Ding, A Generalization Of The Poincare-Birkho Theorem, Proc.Am.Math Soc. 88(1983),341-346.

[4] J.Franks, Recurrence and xed points of surface homeomorphisms, Ergod.Th.& Dynam.Sys. 8(1988),99-107 .

[5] P.Hartman, On boundary value problems for superlinear second order differential equation, J.Di.Eqns 23(1977),37-53.

[6] H.Jacobowitz, periodic solutions of x''+ f(t,x) = 0 via the Poincare-Birkhoff Theorem, J.Diff.Eqns 20(1976),37-52.